C++求sinx的n阶积分从0-PI/2

#include<iostream>
#include<string>
#define PI 3.14
using namespace std;
double result(int n){
  double temp,outcome=1;
  temp=n;
    if(n==1){
    outcome=1;
  }
  else if(n%2==0){
    while(n>=2){
      temp=(n*1.0-1)/n;
      outcome*=temp;
      --n;
    }
    outcome*PI/2;
  }
  else{
    while(n>=3){
      temp=(n*1.0-1.0)/n;
      outcome*=temp;
      --n; 
    }
    outcome*1;
  }
  return outcome;
}
int main(){
  int n,flag=0;
  bool test=true;
  string s;
  cout<<"计算n阶sin(x))从0到PI/2的积分"<<"\n"<<"输入格式：输入sin(x),再换行输入一个数n:"<<endl;
  while(test)
  {
  cin>>s;
  cin>>n;
  if(s=="sin(x)"){
    flag=1;
  }
  switch (flag)
  {
    case 1:
      cout<<"sin(x)的"<<n<<"阶从0-PI/2的积分："<<result(n)<<endl;
      break;
    default:
      cout<<"输入错误"; 
      break; 
  }
  cout<<"继续计算输入数字1，结束输入数字0"<<endl;
  int demo;
  cin>>demo;
  if(demo!=1&&demo!=0){
    cout<<"指令错误重新输入1或者0"<<endl;
    cin>>demo;
  }
  if(demo==1){
    test=true;
    cout<<"开始输入："<<endl; 
  }
  if(demo==0){
    test=false;
  }
  }
  return 0;
}